Finite Group Databasebeta

← #36369067

Subgroups — #36369067

Order 22144.

246 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#26012509C212yesmaximal, complemented
2#26012351C212yesmaximal, complemented
3#26012349C212yesmaximal, complemented
4#26012040C211yesmaximal, characteristic
5#19149746C2214yes—
6#19149736—22no—
7C4×#13063443—22no—
8C2×#14583827C411yescharacteristic
9C2×#14583825C411yescharacteristic
10#19149677C2211yescharacteristic
11#19149675C2211yescharacteristic
12#19149667C411yescharacteristic
13#19149652—22no—
14#19149639—22no—
15C42×D173C2211yescharacteristic
16#124×C173C411yescharacteristic
17C2×#13063443—24no—
18#14583827—42no—
19#14583825—42no—
20C2×Dic346C2×C411yescharacteristic
21C2×D692—21no—
22C2×D692C2×C411yescharacteristic
23C2×C22⋊D173—21no—
24C2×C22⋊D173—22no—
25C22×Dic173—21no—
26C2×C4×D173—21no—
27C2×C4×D173C2×C411yescharacteristic
28C2×C4×D173D412yes—
29#14583805—22no—
30#14583803—22no—
31C4×Dic173D412yes—
32C4×Dic173C2311yescharacteristic
33C2×Q8×C173C2×C411yescharacteristic
34C2×D4×C173C2×C411yescharacteristic
35C22⋊C4×C173—22no—
36C42×C173C2×C411yescharacteristic
37#13063443—44no—
38C22×D173—21no—
39C22×D173C22⋊C411yescharacteristic
40Dic346—41no—
41D692—41no—
42D692—42no—
43C22⋊D173—42no—
44C22⋊D173—44no—
45C2×Dic173—21no—
46C2×Dic173—42no—
47C2×Dic173C22⋊C411yescharacteristic
48C2×Dic173C2×D412yes—
49C4×D173—22no—
50C4×D173—24no—
51C4×D173—42no—
52C23×C173—21no—
53Q8×C173—41no—
54D4×C173—41no—
55C2×C4×C173—21no—
56C2×C4×C173C22⋊C412yes—
57C2×C4×C173C22×C411yescharacteristic
58C22×C173—41no—
59C22×C173—42no—
60C22×C173C2×C22⋊C411yescharacteristic
61C2×D173—21no—
62C2×D173—22no—
63C2×D173—41no—
64C2×D173—42no—
65C4×C173—21no—
66C4×C173—22no—
67C4×C173—41no—
68Dic173—41no—
69Dic173#10012yes—
70Dic173#13514yes—
71C2×C173—81no—
72C2×C173C2×#10011yescharacteristic
73C2×C173#41612yes—
74D173—41no—
75D173—81no—
76C173#154311yescharacteristic, complemented, Sylow
77#1543—1731nomaximal, Sylow
78#532—1731no—
79#431—1732no—
80#333—1732no—
81#331—1732no—
82C2×#41—1731no—
83C2×#41—1731no—
84C4⋊Q8—1731no—
85#127—1731no—
86#124—1731no—
87#124#1062192411yescharacteristic
88#121—3462no—
89C4×D4—3462no—
90C2×C42—1731no—
91C4⋊C8—1734no—
92C22⋊C8—3462no—
93C4×C8—3462no—
94#41—6922no—
95#41—6922no—
96C2×Q8—1731no—
97C2×Q8C2×#1062192411yescharacteristic
98C2×D4—3461no—
99C2×D4—3461no—
100C2×D4—3462no—
101C2×D4—1731no—
102C2×D4C2×#1062192411yescharacteristic
103C22×C4—3461no—
104C22×C4—3461no—
105C22×C4—1732no—
106C22×C4—1731no—
107C2×C8—3464no—
108C4⋊C4—3462no—
109C22⋊C4—22no—
110C22⋊C4—3462no—
111C42—1732no—
112C42—1731no—
113C42C2×#1062192411yescharacteristic
114C23—21no—
115C23—3461no—
116C23—1731no—
117Q8—41no—
118Q8—6921no—
119D4—41no—
120D4—6921no—
121D4—6922no—
122D4—6924no—
123D4—6922no—
124C2×C4—21no—
125C2×C4—3464no—
126C2×C4—3462no—
127C2×C4—3461no—
128C2×C4—1731no—
129C2×C4—1732no—
130C2×C4—6922no—
131C2×C4—6922no—
132C2×C4C22⋊#1062192412yes—
133C2×C4C22×#1062192411yescharacteristic
134C8—6924no—
135C22—41no—
136C22—42no—
137C22—3461no—
138C22—3462no—
139C22—6921no—
140C22—6922no—
141C22C2×C22⋊#1062192411yescharacteristic
142C4—21no—
143C4—22no—
144C4—41no—
145C4—1732no—
146C4—1734no—
147C4—6921no—
148C2—81no—
149C2—13841no—
150C2—6921no—
151C2D173⋊#10011yescharacteristic
152C2#2601248112yes—
subgroupG/H
centerC22C2×C22⋊#10621924
commutatorC2×C4×C173C22×C4
FrattiniC2×C4C22×#10621924
Fitting#124×C173C4
socleC22×C173C2×C22⋊C4
prime radical#26012040C2
cosocleC4×Dic173C23
hypercenter#124#10621924
hypocenterC173#1543
LCSG ▷ C2×C4×C173 ▷ C22×C173 ▷ C173
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #26012509C2semidirect
2. #26012351C2semidirect
3. #26012349C2semidirect
76. C173#1543semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#260125092
#260123512
#260123492
#260120402
#1543173